Bringing in Multiple Animations of a Single Armature to Be Used For One Animation
Assuming you're in the file you'd like to combine the actions in:


Goto File >> Append
In the file manager, navigate to the file with the walk/run/front flip.
Click on the actual .blend, you'll see a bunch of datablock categories (Action, Mesh, etc).
Click on Action.
Select on the action you want to import, and click Append.
You should be able to load this action in the Dopesheet/NLA now.  Note that this action won't update from the original file.  If you wanted that, do the above, except clicking Append on the menu, click Link.